Question: Simplify the following expression: $ t = 3 - \dfrac{1}{z + 7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z + 7}{z + 7}$ $ \dfrac{3}{1} \times \dfrac{z + 7}{z + 7} = \dfrac{3z + 21}{z + 7} $ Therefore $ t = \dfrac{3z + 21}{z + 7} - \dfrac{1}{z + 7} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{3z + 21 - 1 }{z + 7} $ Distribute the negative sign: $t = \dfrac{3z + 21 - 1}{z + 7}$ $t = \dfrac{3z + 20}{z + 7}$